1 = 0.999

1 = 0.99999

Algebraic proof -

Let's say x = 0.999999(infinitely)

1 = x (Start with an assumption)

10 = 10x

10 - 1 = 10x - x =9.9999(infinitely) - 0.99999(infinitely) = 9

9 = 9

We haven't reached a Reductio Ad Absurdum so our assumption must have been true, which means that

1=0.99(Infinitely)\boxed{1 = 0.99(Infinitely)}

Note by A Former Brilliant Member
1 month, 2 weeks ago

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1 vote

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Comments

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Hahaha! Check this problem :-)

Páll Márton - 1 month, 2 weeks ago

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Vinayak used the same Logic. :)

A Former Brilliant Member - 1 month, 2 weeks ago

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Yeah. What about my solution?

Páll Márton - 1 month, 2 weeks ago

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@Páll Márton Nice, I never thought of the infinite series like that. Awesome!!

A Former Brilliant Member - 1 month, 2 weeks ago

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@Páll Márton I upvoted!! :-)

A Former Brilliant Member - 1 month, 2 weeks ago

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@A Former Brilliant Member Thank you!

Páll Márton - 1 month, 2 weeks ago

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@Páll Márton First, i didn't understand why you took 1.8, then I understood, - 1.8 + 0.18 = 1.99. Nice!! Your solution is the best!!

A Former Brilliant Member - 1 month, 2 weeks ago

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@Páll Márton I put a shimmering heart emoji on it as a comment.

A Former Brilliant Member - 1 month, 2 weeks ago

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@A Former Brilliant Member Thank you!

Páll Márton - 1 month, 2 weeks ago

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@Páll Márton Well - what can I do?...

A Former Brilliant Member - 1 month, 2 weeks ago

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@A Former Brilliant Member To fix bread on the tree?

Páll Márton - 1 month, 2 weeks ago

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@Páll Márton Seriously? Also, did you see my comment on Did I see something in my dreams? (I)

A Former Brilliant Member - 1 month, 2 weeks ago

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@A Former Brilliant Member Yes. some text\color{#FFFFFF}\text{some text}

Páll Márton - 1 month, 2 weeks ago

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@A Former Brilliant Member Can you explain your plans?

Páll Márton - 1 month, 2 weeks ago

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@Páll Márton Let me give you a taster on one of them:

Imagine a clock, but 10,11,1210, 11, 12 has been replaced by A,B,CA, B, C.

What's 11:1011:10 in hexadecimal time?

Give your answer in 55 minutes.

A Former Brilliant Member - 1 month, 2 weeks ago

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@Páll Márton 11 minute left.

A Former Brilliant Member - 1 month, 2 weeks ago

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@Páll Márton Time's up. The answer is B:AB:A because:

11=B,10=A11 = B, 10 = A

A Former Brilliant Member - 1 month, 2 weeks ago

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@Páll Márton I hope you get my plans now.

A Former Brilliant Member - 1 month, 2 weeks ago

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@A Former Brilliant Member Sorry! I was just helping my mom.

Páll Márton - 1 month, 2 weeks ago

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@Páll Márton I know what is the hexadecimal numbers.

Páll Márton - 1 month, 2 weeks ago

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@Páll Márton No worries - I understand. But I hope you now know what I am going to do - problems with them!

First Hexadecimal Clock Problem will be posted today, 13:4513:45pm

First Binary Clock Problem will be posted tomorrow, 10:3010:30am

The other two (Algebraic Binary Locks and Algebraic Hexadecimal Locks) will be used later in the summer...

A Former Brilliant Member - 1 month, 2 weeks ago

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@A Former Brilliant Member Ok. I'm waiting...

Páll Márton - 1 month, 2 weeks ago

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@Páll Márton Note - I am using a traditional clock as the base/template for this problem.

A Former Brilliant Member - 1 month, 2 weeks ago

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@Páll Márton

Páll Márton - 1 month, 2 weeks ago

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@Páll Márton 😒😕😑😐🤦🤨, @Páll Márton

A Former Brilliant Member - 1 month, 2 weeks ago

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@Páll Márton es that yu @Páll Márton because yu Hungarian, are yu youtuber?

A Former Brilliant Member - 1 month, 2 weeks ago

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@A Former Brilliant Member No. JustVidman is a famous youtuber in Hungary. He has 629k subscribers and only 15M people speak hungarian so 4%4\%. This is equal if he speak in english, then 700M629k15M=29M700M\cdot \frac{629k}{15M}=29M subscribers.

Páll Márton - 1 month, 2 weeks ago

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@Páll Márton Oh, cool!!

A Former Brilliant Member - 1 month, 2 weeks ago

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This is not a right way to prove, there is a way called proof by contradiction, but if from an assumption. If you haven't reached to a contradiction yet this doesn't mean that the assumption was correct. Maybe a contradiction may come out after sometime.

Zakir Husain - 1 month, 2 weeks ago

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My solution is bad or the Former Brilliant Member's solution is bad?

Páll Márton - 1 month, 2 weeks ago

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Former Brilliant Member's solution is bad, because he wanted to explain this

Let x = 0.999.....\text{x = 0.999.....}

10x = 9.999.....\text{10x = 9.999.....}

10x = 9 + 0.999.....\text{10x = 9 + 0.999.....}

10x = 9 + x\text{10x = 9 + x}

9x = 9\text{9x = 9}

x = 1\text{x = 1}

1 = 0.999.....\text{1 = 0.999.....}

but did it in the wrong way

A Former Brilliant Member - 1 month, 2 weeks ago

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